Exasperated, Mr. Rice put down the iPad. “Listen to what this moron says. This is what I was running against!” He described gasps of disbelief at a campaign stop at the same country club when he matter-of-factly declared that Mr. Trump had lost the election. “It was painful.”

In July, he lost this primary after receiving less than a quarter of the vote. In the 2020 general election, he had coasted to victory with 62 percent.

In an interview, Mr. Meijer, who had also voted to impeach and lost his primary, said he was surprised Republicans had not suffered a backlash from voters over the objections and the Jan. 6 riot. He argued that the leftward-tilt of the Biden administration had pushed voters back toward Mr. Trump, citing executive orders that stretched the authority of the White House to impose vaccine mandates, an eviction moratorium and the cancellation of student debt.

“These massive uses of executive power,” he said, “make people feel like, if you are not with us pushing on the brake pedal, then you are de facto helping the Democratic majority push on the gas.”

Objectors who doubled down have thrived.

Mr. Budd of North Carolina signaled support for Mr. Trump’s fraud claims in the weeks after the election by introducing the Combat Voter Fraud Act. As a Republican candidate for the Senate, he warmed up a Trump rally this spring by accusing Democrats of opposing “election integrity” because “they know they can’t win elections on a woke left agenda.” (A spokesman for Mr. Budd said he had started pushing for tighter voter registration requirements long before the 2020 election, noting the experience of a major election fraud scandal in his state in 2018.)

In Oklahoma, Mr. Mullin stood out from the pack of Republican Senate candidates by introducing a bill to officially expunge Mr. Trump’s second impeachment. It faulted the Democratic impeachment leaders for failing to note the “unusual voting patterns” and “voting anomalies of the 2020 presidential election,” or to understand why Republicans doubted that Mr. Trump had “not won re-election.” The resolution, co-sponsored by more than 30 lawmakers, did not advance, but it curried favor with the former president. In July, Mr. Trump officially endorsed Mr. Mullin.

Mr. Mullin, who owns a ranch, spent a hot Saturday that same month campaigning among his fellow cattlemen at their annual conference in Norman, Okla. One attendee, Joel Reimer, applauded him for taking a stand against the Electoral College count knowing he would be ridiculed by many for buying into conspiracy theories. Mr. Reimer, who manages a beef ranch, added, “From a small-town guy’s perspective, I personally had questions about the validity of the vote.”

The campaign gave out fliers declaring that “no one in Congress has worked harder to SAVE AMERICA” and proclaiming Mr. Mullin “TRUMP-TOUGH.” At the top of a checklist of priorities was the party’s new refrain: “Secure our elections.”

Reporting was contributed by Amudalat Ajasa, Michael H. Keller, Aimee Ortiz, Rachel Shorey and Julie Tate. Produced by Sean Catangui and Hang Do Thi Duc.

The Times drew on data from various sources to analyze the 139 objectors, including from the A-Mark Foundation, Ballotpedia, CQ, The Cook Political Report, Daily Kos, L2 and LegiStorm. Data analysis was also contributed by Andrew Beveridge and Susan Weber of SocialExplorer.com.